Halve and pit the avocados, then mash them in a small mixing bowl with a fork or masher until mostly smooth.
Add the minced garlic, lime juice (from 1/2 lime), ground cumin, crushed red pepper, sea salt, and cracked pepper to the mashed avocado and stir to combine.
Fold in the chopped cilantro, rinsed black beans, corn, and diced red onion until evenly distributed.
Heat 1 tablespoon olive oil in a skillet over medium heat.
While the pan heats, place half of the avocado mixture on one half of a tortilla, then fold the other half over to close; repeat with remaining tortilla and filling.
Place a folded quesadilla in the hot skillet and cook until the bottom is browned and crisp, about 2–3 minutes.
Flip the quesadilla and cook the other side until browned, about 2 more minutes. Repeat with the second quesadilla.
Transfer to a cutting board and gently slice each quesadilla; serve immediately.